In known compression connections, as they are, for example, described in U.S. Pat. No. 4,328,982, the compression sleeve has an inner serration, which enters due to the force applied for producing the connection, the outer wall of the pipe. Thus, different and even conflicting material requirements for the respective portions of the compression sleeve result. The tubular outer portion of the compression sleeve, which is acted upon by the force, has to be deformed and requires a ductile material. After the pressing, the pipe as well as the compression sleeve relax according to the elastic deformation portion. To produce a radial pre-biasing between the compression sleeve and the pipe, the elastic relaxation of the compression sleeve has to be smaller than the elastic relaxation of the pipe. This can be achieved by a compression sleeve material of lower strength compared to the pipe material. However, for the serration of the compression sleeve, rather a material of high strength and hardness is required, to ensure the penetration into the pipe material. A disadvantage of the state of the art results from this inconsistency.